Use our free GCF of Fractions Calculator tool to compute the GCF of 407/342, 1349/926 i.e 1/158346 easily. The following is the detailed procedure to determine the greatest common factor of fractions 407/342, 1349/926.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 407/342,1349/926
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 407/342,1349/926, numerators are 407,1349
Denominators are 342,926
The GCF of 407,1349 is 1 .
LCM of 342,926 is 158346.
The greatest common factor of 407/342,1349/926 = [GCF of 407,1349]/[LCM of 342,926]= 1/158346
Therefore, the GCF of 407/342,1349/926 is 1/158346.
To find the highest common factor of 407,1349, we have to find the factors of both numbers and list the highest common factor.
The factors of 407 are 1, 11, 37, 407
The factors of 1349 are 1, 19, 71, 1349
The HCF of 407,1349 is 1.
Lets's calculate GCF of 407,1349
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 407
:1,11,37,407
Now, list down the factors of 1349
:1,19,71,1349
Greatest Common Factor
We found the factors 407,1349 . The biggest common factor number is the GCF number.
So the greatest common factor 407,1349 is 1.
Lets's calculate LCM of 342,926
2 | 342, 926 |
171, 463 |
∴ So the LCM of the given numbers is 2 x 171 x 463 = 158346
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/158346
Therefore, the GCF of Fractions 407/342,1349/926 is 1/158346
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 342,926 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(342,926) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(342,926) x common factors =2 x 1 = 2
LCM(342,926) = ( 342 × 926 ) / 2
LCM(342,926) = 316692 / 2
LCM(342,926) = 158346
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 407,1349?
The HCF of 407,1349 is 1
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 407/342, 1349/926?
Answer: GCF of Numerators as per given numbers 407/342, 1349/926 is
GCF of Numerators i.e. for 407,1349 is 1
LCM of denominators i.e. for 342,926 is 158346.
Thus, GCF of Fractions is 1/158346.Finally, GCF of Fractions for 407/342, 1349/926 is 1/158346.